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I was wondering about the size of the Jordan blocks of the following matrix.

$$\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 0 & 0 & 0 \end{bmatrix}$$

I know that Jordan blocks have $1$'s on the superdiagonal. So are these $3$ blocks of size $1 \times 1$ or is this one block of size $3 \times 3$? I'm not sure how to tell the difference. Thanks in advance.

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If this was three 1×1 blocks, there wouldn't be any non-zero values off the main diagonal (because a 1×1 block is just the eigenvalue itself), so this must be one 3×3 block with corresponding eigenvalue zero.

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